ODE No. 1589

  1. Problem in Latex
  2. Mathematica input
  3. Maple input

\[ x^{11/2} y^{(11)}(x)-a y(x)=0 \] Mathematica : cpu = 0.047046 (sec), leaf count = 670

\[\left \{\left \{y(x)\to \frac {4}{121} (-1)^{2/11} a^{2/11} c_2 x \, _0F_{10}\left (;-\frac {7}{11},-\frac {5}{11},-\frac {3}{11},-\frac {1}{11},\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11};\frac {2048 a x^{11/2}}{285311670611}\right )-\frac {1048576 (-1)^{9/11} a^{20/11} c_{11} x^{10} \, _0F_{10}\left (;\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11},\frac {23}{11},\frac {25}{11},\frac {27}{11},\frac {29}{11},\frac {31}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{672749994932560009201}-\frac {262144 (-1)^{7/11} a^{18/11} c_{10} x^9 \, _0F_{10}\left (;\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11},\frac {23}{11},\frac {25}{11},\frac {27}{11},\frac {29}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{5559917313492231481}-\frac {65536 (-1)^{5/11} a^{16/11} c_9 x^8 \, _0F_{10}\left (;\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11},\frac {23}{11},\frac {25}{11},\frac {27}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{45949729863572161}-\frac {16384 (-1)^{3/11} a^{14/11} c_8 x^7 \, _0F_{10}\left (;\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11},\frac {23}{11},\frac {25}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{379749833583241}-\frac {4096 \sqrt [11]{-1} a^{12/11} c_7 x^6 \, _0F_{10}\left (;\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11},\frac {23}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{3138428376721}+\frac {1024 (-1)^{10/11} a^{10/11} c_6 x^5 \, _0F_{10}\left (;\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11},\frac {21}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{25937424601}+\frac {256 (-1)^{8/11} a^{8/11} c_5 x^4 \, _0F_{10}\left (;-\frac {1}{11},\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11},\frac {19}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{214358881}+\frac {64 (-1)^{6/11} a^{6/11} c_4 x^3 \, _0F_{10}\left (;-\frac {3}{11},-\frac {1}{11},\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11},\frac {17}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{1771561}+\frac {16 (-1)^{4/11} a^{4/11} c_3 x^2 \, _0F_{10}\left (;-\frac {5}{11},-\frac {3}{11},-\frac {1}{11},\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11},\frac {13}{11},\frac {15}{11};\frac {2048 a x^{11/2}}{285311670611}\right )}{14641}+c_1 \, _0F_{10}\left (;-\frac {9}{11},-\frac {7}{11},-\frac {5}{11},-\frac {3}{11},-\frac {1}{11},\frac {1}{11},\frac {3}{11},\frac {5}{11},\frac {7}{11},\frac {9}{11};\frac {2048 a x^{11/2}}{285311670611}\right )\right \}\right \}\] Maple : cpu = 10.253 (sec), leaf count = 4353

\[ \left \{ y \left ( x \right ) =-3780\,{\frac {1}{\sqrt {x}} \left ( \left ( \left ( -4/9\,{x}^{3/2} \left ( \left ( -{\it \_C9}+{\it \_C3}-3\,{\it \_C5}+3/2\,{\it \_C6} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( 3\,{\it \_C7}-{\it \_C8}-3\,{\it \_C10}+{\it \_C4} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( 3\,{\it \_C8}-3\,{\it \_C9}+{\it \_C10}-{\it \_C5} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\frac {{\it \_C11}}{6930}}+{\it \_C1}+3\,{\it \_C4} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -4\,{\it \_C2}+3\,{\it \_C3}+{\it \_C6}/2 \right ) \cos \left ( \pi /11 \right ) +{\frac {{\it \_C11}}{20790}}+3\,{\it \_C1} \right ) {a}^{2/11}-2/9\, \left ( \left ( {\it \_C7}-3\,{\it \_C10}+{\frac {{\it \_C11}}{6930}}+{\it \_C4} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( 3\,{\it \_C8}-{\it \_C9}-{\it \_C5}+3/2\,{\it \_C6} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( 3\,{\it \_C7}-{\it \_C8}+3\,{\it \_C9}-{\it \_C10} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -3\,{\it \_C2}+{\it \_C3}-3\,{\it \_C5}+{\it \_C6}/2 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\frac {{\it \_C11}}{20790}}+4\,{\it \_C1}+3\,{\it \_C4} \right ) \cos \left ( \pi /11 \right ) -{\it \_C2}+3\,{\it \_C3} \right ) {x}^{2}{a}^{3/11}-{\frac {4\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( 3\,{\it \_C8}-3\,{\it \_C2}-{\it \_C5}+{\it \_C6}/2 \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}+3\,{\it \_C9}-{\it \_C10}+{\frac {{\it \_C11}}{6930}} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -3\,{\it \_C7}+{\it \_C8}-{\it \_C9}+3/2\,{\it \_C6} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -3\,{\it \_C10}+{\frac {{\it \_C11}}{20790}}+3\,{\it \_C1}+{\it \_C4} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -{\it \_C2}+4\,{\it \_C3}-3\,{\it \_C5} \right ) \cos \left ( \pi /11 \right ) +{\it \_C1}+3\,{\it \_C4} \right ) }+{\frac {8\,{x}^{3}}{315} \left ( \left ( -{\it \_C9}+{\it \_C10}/3-{\frac {{\it \_C11}}{62370}}-{\it \_C1} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C8}/3+{\it \_C2}-{\it \_C6}/6 \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C7}/3-{\it \_C9}/3-{\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C8}+{\it \_C2}/3-{\it \_C3}+{\it \_C5}/3 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C10}-{\it \_C1}/3-4/3\,{\it \_C4} \right ) \cos \left ( \pi /11 \right ) -{\it \_C3}/3+{\it \_C5} \right ) {a}^{{\frac {5}{11}}}}+ \left ( -3/2\, \left ( {\it \_C4}+{\it \_C7}-{\it \_C8}/3+{\it \_C1}/3 \right ) x{a}^{1/11}+3/4\, \left ( -{\it \_C10}/3+{\it \_C2}/3+{\it \_C9}-{\it \_C3} \right ) \sqrt {x} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( 3/2\, \left ( {\it \_C5}-{\it \_C10}/3-{\it \_C3}/3+{\it \_C9} \right ) x{a}^{1/11}+3/4\,\sqrt {x} \left ( -{\it \_C5}/3+{\it \_C8}-{\it \_C4}-{\it \_C1}/3 \right ) \right ) \cos \left ( 4/11\,\pi \right ) + \left ( 3/2\,x \left ( -{\it \_C4}/3-{\it \_C5}/3+{\it \_C8}+{\it \_C10} \right ) {a}^{1/11}-3/4\, \left ( {\it \_C10}-{\it \_C5}+{\it \_C3}/3-{\it \_C4}/3 \right ) \sqrt {x} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 1/2\, \left ( {\it \_C9}+{\it \_C2}-3\,{\it \_C3}-3/2\,{\it \_C6} \right ) x{a}^{1/11}-3/4\, \left ( -{\it \_C8}/3+{\it \_C7}+{\it \_C1} \right ) \sqrt {x} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -1/2\, \left ( {\it \_C7}+3\,{\it \_C1}+{\frac {2\,{\it \_C11}}{10395}} \right ) x{a}^{1/11}+1/4\,\sqrt {x} \left ( -2\,{\it \_C6}+3\,{\it \_C2}+{\it \_C9} \right ) \right ) \cos \left ( \pi /11 \right ) +3/2\, \left ( {\it \_C2}-{\it \_C6}/6 \right ) x{a}^{1/11}-1/4\,\sqrt {x} \left ( {\frac {2\,{\it \_C11}}{10395}}+{\it \_C7} \right ) \right ) \cos \left ( 2\,\sin \left ( \pi /11 \right ) {a}^{1/11}\sqrt {x} \right ) -3/4\, \left ( {\frac {16\,{x}^{3/2}{a}^{2/11}}{27} \left ( \left ( -{\it \_C9}-{\it \_C3}+3\,{\it \_C5}+3/2\,{\it \_C6} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( 3\,{\it \_C7}-{\it \_C8}+3\,{\it \_C10}-{\it \_C4} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -3\,{\it \_C8}-3\,{\it \_C9}+{\it \_C10}+{\it \_C5} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\frac {{\it \_C11}}{6930}}-{\it \_C1}-3\,{\it \_C4} \right ) \sin \left ( 2/11\,\pi \right ) -2\, \left ( {\it \_C2}+3/2\,{\it \_C3}-{\it \_C6}/4 \right ) \sin \left ( \pi /11 \right ) \right ) }+{\frac {8\,{a}^{3/11}{x}^{2}}{27} \left ( \left ( {\it \_C7}+3\,{\it \_C10}+{\frac {{\it \_C11}}{6930}}-{\it \_C4} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -3\,{\it \_C8}-{\it \_C9}+{\it \_C5}+3/2\,{\it \_C6} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( 3\,{\it \_C7}-{\it \_C8}-3\,{\it \_C9}+{\it \_C10} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -3\,{\it \_C2}-{\it \_C3}+3\,{\it \_C5}+{\it \_C6}/2 \right ) \sin \left ( 2/11\,\pi \right ) +{\frac {\sin \left ( \pi /11 \right ) \left ( {\it \_C11}+41580\,{\it \_C1}-62370\,{\it \_C4} \right ) }{20790}} \right ) }+{\frac {16\,{x}^{5/2}{a}^{4/11}}{189} \left ( \left ( -3\,{\it \_C8}-3\,{\it \_C2}+{\it \_C5}+{\it \_C6}/2 \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}-3\,{\it \_C9}+{\it \_C10}+{\frac {{\it \_C11}}{6930}} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( 3\,{\it \_C7}-{\it \_C8}-{\it \_C9}+3/2\,{\it \_C6} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 3\,{\it \_C10}+{\frac {{\it \_C11}}{20790}}+3\,{\it \_C1}-{\it \_C4} \right ) \sin \left ( 2/11\,\pi \right ) -\sin \left ( \pi /11 \right ) \left ( {\it \_C2}-2\,{\it \_C3}-3\,{\it \_C5} \right ) \right ) }+{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\it \_C9}+{\it \_C10}/3+{\frac {{\it \_C11}}{62370}}+{\it \_C1} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C8}/3-{\it \_C2}+{\it \_C6}/6 \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C7}/3-{\it \_C9}/3+{\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C8}-{\it \_C2}/3+{\it \_C3}+{\it \_C5}/3 \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C10}+{\it \_C1}/3+2/3\,{\it \_C4} \right ) \right ) {a}^{{\frac {5}{11}}}}+ \left ( 2\, \left ( -{\it \_C4}+{\it \_C7}-{\it \_C1}/3-{\it \_C8}/3 \right ) x{a}^{1/11}-\sqrt {x} \left ( -{\it \_C2}/3+{\it \_C9}-{\it \_C10}/3+{\it \_C3} \right ) \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -2\, \left ( -{\it \_C5}-{\it \_C10}/3+{\it \_C3}/3+{\it \_C9} \right ) x{a}^{1/11}-\sqrt {x} \left ( {\it \_C1}/3-{\it \_C5}/3+{\it \_C8}+{\it \_C4} \right ) \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -2\, \left ( {\it \_C8}+{\it \_C4}/3-{\it \_C5}/3-{\it \_C10} \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C3}/3+{\it \_C10}-{\it \_C4}/3+{\it \_C5} \right ) \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -2/3\, \left ( {\it \_C9}-{\it \_C2}+3\,{\it \_C3}-3/2\,{\it \_C6} \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C8}/3-{\it \_C1}+{\it \_C7} \right ) \right ) \sin \left ( 2/11\,\pi \right ) +2/3\, \left ( x \left ( {\it \_C7}+{\frac {{\it \_C11}}{10395}}-3\,{\it \_C1} \right ) {a}^{1/11}-1/2\,\sqrt {x} \left ( {\it \_C9}-3\,{\it \_C2}-{\it \_C6} \right ) \right ) \sin \left ( \pi /11 \right ) \right ) \sin \left ( 2\,\sin \left ( \pi /11 \right ) {a}^{1/11}\sqrt {x} \right ) \right ) {{\rm e}^{-2\,\cos \left ( \pi /11 \right ) {a}^{1/11}\sqrt {x}}}+ \left ( \left ( {\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C7}-{\it \_C10} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -{\frac {{\it \_C11}}{20790}}-{\it \_C4} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C5}-{\it \_C6}/2 \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C2}+{\it \_C3} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -{\it \_C8}+{\it \_C9} \right ) \cos \left ( \pi /11 \right ) -{\it \_C1} \right ) }-{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( -{\it \_C8}-{\it \_C6}/2 \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -{\it \_C2}-{\it \_C5} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C10}+{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C1}-{\it \_C4} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C9} \right ) \cos \left ( \pi /11 \right ) +{\it \_C3} \right ) }+{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C9}+{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C10}-{\it \_C1} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C8}+{\it \_C2} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C3}-{\it \_C5} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C6}/2 \right ) \cos \left ( \pi /11 \right ) -{\it \_C4} \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( {\it \_C7}+{\it \_C2} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C8}+{\it \_C3} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C9}+{\it \_C1} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C10}-{\it \_C4} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\frac {{\it \_C11}}{20790}}-{\it \_C6}/2 \right ) \cos \left ( \pi /11 \right ) -{\it \_C5} \right ) {a}^{{\frac {5}{11}}}}+ \left ( -2\,x \left ( {\it \_C9}+{\it \_C5} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C8}-{\it \_C4} \right ) \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -2\, \left ( {\it \_C3}+{\it \_C6}/2 \right ) x{a}^{1/11}-\sqrt {x} \left ( {\it \_C7}+{\it \_C1} \right ) \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C7}+{\it \_C4} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C9}-{\it \_C3} \right ) \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\frac {x \left ( 20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}-\sqrt {x} \left ( -{\it \_C6}/2+{\it \_C2} \right ) \right ) \cos \left ( 2/11\,\pi \right ) + \left ( 2\,x \left ( {\it \_C8}+{\it \_C10} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C10}-{\it \_C5} \right ) \right ) \cos \left ( \pi /11 \right ) -{\frac {{\it \_C11}\,\sqrt {x}}{20790}}+2\,{\it \_C2}\,{a}^{1/11}x \right ) \cos \left ( 2\,\sin \left ( 2/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) +\sin \left ( 2\,\sin \left ( 2/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) \left ( {\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C7}+{\it \_C10} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\frac {{\it \_C11}}{20790}}-{\it \_C4} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -{\it \_C5}-{\it \_C6}/2 \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C2}+{\it \_C3} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C8}+{\it \_C9} \right ) \right ) }-{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( {\it \_C8}-{\it \_C6}/2 \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C2}-{\it \_C5} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C10}+{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C1}-{\it \_C4} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C7}-{\it \_C9} \right ) \right ) }-{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C10}-{\it \_C1} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -{\it \_C8}-{\it \_C2} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C3}+{\it \_C5} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C7}+{\it \_C6}/2 \right ) \right ) }+{\frac {32\,{x}^{3}}{945} \left ( \left ( {\it \_C7}-{\it \_C2} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C8}+{\it \_C3} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C9}-{\it \_C1} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C10}-{\it \_C4} \right ) \sin \left ( 2/11\,\pi \right ) -{\frac {\sin \left ( \pi /11 \right ) \left ( {\it \_C11}+10395\,{\it \_C6} \right ) }{20790}} \right ) {a}^{{\frac {5}{11}}}}+ \left ( -2\,x \left ( {\it \_C9}-{\it \_C5} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C8}+{\it \_C4} \right ) \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -2\, \left ( {\it \_C3}-{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C1}+{\it \_C7} \right ) \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C7}-{\it \_C4} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C9}+{\it \_C3} \right ) \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\frac {x \left ( -20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}- \left ( {\it \_C2}+{\it \_C6}/2 \right ) \sqrt {x} \right ) \sin \left ( 2/11\,\pi \right ) +2\,\sin \left ( \pi /11 \right ) \left ( x \left ( {\it \_C8}-{\it \_C10} \right ) {a}^{1/11}-1/2\,\sqrt {x} \left ( {\it \_C10}+{\it \_C5} \right ) \right ) \right ) \right ) {{\rm e}^{2\,\cos \left ( 2/11\,\pi \right ) {a}^{1/11}\sqrt {x}}}+ \left ( \left ( {\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C2}-{\it \_C3} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C8}-{\it \_C9} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\frac {{\it \_C11}}{20790}}+{\it \_C4} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C5}+{\it \_C6}/2 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C10} \right ) \cos \left ( \pi /11 \right ) -{\it \_C1} \right ) }+{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( -{\it \_C1}-{\it \_C4} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C9} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C2}-{\it \_C5} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C10}+{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C8}+{\it \_C6}/2 \right ) \cos \left ( \pi /11 \right ) -{\it \_C3} \right ) }-{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C3}-{\it \_C5} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C6}/2 \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C10}-{\it \_C1} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C8}+{\it \_C2} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -{\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( \pi /11 \right ) +{\it \_C4} \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\it \_C10}+{\it \_C4} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -{\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C8}-{\it \_C3} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C9}-{\it \_C1} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C2} \right ) \cos \left ( \pi /11 \right ) -{\it \_C5} \right ) {a}^{{\frac {5}{11}}}}+ \left ( -{\frac {x \left ( 20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}+\sqrt {x} \left ( -{\it \_C6}/2+{\it \_C2} \right ) \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C8}+{\it \_C10} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C10}-{\it \_C5} \right ) \right ) \cos \left ( 4/11\,\pi \right ) + \left ( 2\, \left ( {\it \_C3}+{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( {\it \_C7}+{\it \_C1} \right ) \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 2\,x \left ( {\it \_C7}+{\it \_C4} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C9}-{\it \_C3} \right ) \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C9}+{\it \_C5} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C8}-{\it \_C4} \right ) \right ) \cos \left ( \pi /11 \right ) -{\frac {{\it \_C11}\,\sqrt {x}}{20790}}+2\,{\it \_C2}\,{a}^{1/11}x \right ) \cos \left ( 2\,\sin \left ( 3/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) - \left ( -{\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C2}+{\it \_C3} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C8}-{\it \_C9} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -{\frac {{\it \_C11}}{20790}}+{\it \_C4} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C5}-{\it \_C6}/2 \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C7}+{\it \_C10} \right ) \right ) }-{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( -{\it \_C1}+{\it \_C4} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C9} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C2}-{\it \_C5} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C10}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( 2/11\,\pi \right ) - \left ( {\it \_C8}-{\it \_C6}/2 \right ) \sin \left ( \pi /11 \right ) \right ) }-{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( -{\it \_C3}-{\it \_C5} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C6}/2 \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -{\it \_C10}-{\it \_C1} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C8}+{\it \_C2} \right ) \sin \left ( 2/11\,\pi \right ) - \left ( {\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( \pi /11 \right ) \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\it \_C10}-{\it \_C4} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C8}-{\it \_C3} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C9}-{\it \_C1} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C7}-{\it \_C2} \right ) \right ) {a}^{{\frac {5}{11}}}}+ \left ( {\frac {x \left ( -20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}+ \left ( {\it \_C2}+{\it \_C6}/2 \right ) \sqrt {x} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( 2\,x \left ( {\it \_C8}-{\it \_C10} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C10}+{\it \_C5} \right ) \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -2\, \left ( {\it \_C3}-{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C1}+{\it \_C7} \right ) \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 2\,x \left ( {\it \_C7}-{\it \_C4} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C9}+{\it \_C3} \right ) \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( 2\,x \left ( {\it \_C9}-{\it \_C5} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C8}+{\it \_C4} \right ) \right ) \right ) \sin \left ( 2\,\sin \left ( 3/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) \right ) {{\rm e}^{-2\,\cos \left ( 3/11\,\pi \right ) {a}^{1/11}\sqrt {x}}}+ \left ( \left ( {\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\frac {{\it \_C11}}{20790}}+{\it \_C4} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -{\it \_C2}+{\it \_C3} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C10} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C8}-{\it \_C9} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C5}-{\it \_C6}/2 \right ) \cos \left ( \pi /11 \right ) -{\it \_C1} \right ) }+{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( -{\it \_C2}-{\it \_C5} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C1}+{\it \_C4} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C8}+{\it \_C6}/2 \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\it \_C9} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C10}-{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( \pi /11 \right ) -{\it \_C3} \right ) }-{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C10}-{\it \_C1} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( -{\it \_C3}+{\it \_C5} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}-{\it \_C6}/2 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C8}-{\it \_C2} \right ) \cos \left ( \pi /11 \right ) +{\it \_C4} \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\it \_C8}-{\it \_C3} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C10}-{\it \_C4} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C2} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C9}+{\it \_C1} \right ) \cos \left ( \pi /11 \right ) -{\it \_C5} \right ) {a}^{{\frac {5}{11}}}}+ \left ( 2\, \left ( {\it \_C3}+{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( {\it \_C7}+{\it \_C1} \right ) \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\frac {x \left ( 20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}-\sqrt {x} \left ( -{\it \_C6}/2+{\it \_C2} \right ) \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C9}+{\it \_C5} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C8}-{\it \_C4} \right ) \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -2\,x \left ( {\it \_C8}+{\it \_C10} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C10}-{\it \_C5} \right ) \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C7}+{\it \_C4} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C9}-{\it \_C3} \right ) \right ) \cos \left ( \pi /11 \right ) -{\frac {{\it \_C11}\,\sqrt {x}}{20790}}+2\,{\it \_C2}\,{a}^{1/11}x \right ) \cos \left ( 2\,\sin \left ( 4/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) +\sin \left ( 2\,\sin \left ( 4/11\,\pi \right ) {a}^{1/11}\sqrt {x} \right ) \left ( -{\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( -{\frac {{\it \_C11}}{20790}}+{\it \_C4} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C2}-{\it \_C3} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C7}+{\it \_C10} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C8}+{\it \_C9} \right ) \sin \left ( 2/11\,\pi \right ) -\sin \left ( \pi /11 \right ) \left ( {\it \_C5}+{\it \_C6}/2 \right ) \right ) }+{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( -{\it \_C2}+{\it \_C5} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C1}+{\it \_C4} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C8}-{\it \_C6}/2 \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}-{\it \_C9} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C10}+{\frac {{\it \_C11}}{20790}} \right ) \right ) }+{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C10}+{\it \_C1} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C3}-{\it \_C5} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\it \_C6}/2 \right ) \sin \left ( 2/11\,\pi \right ) -\sin \left ( \pi /11 \right ) \left ( {\it \_C8}+{\it \_C2} \right ) \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( {\it \_C8}-{\it \_C3} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C10}+{\it \_C4} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C7}-{\it \_C2} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\frac {{\it \_C11}}{20790}}-{\it \_C6}/2 \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C9}-{\it \_C1} \right ) \right ) {a}^{{\frac {5}{11}}}}+ \left ( -2\, \left ( {\it \_C3}-{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C1}+{\it \_C7} \right ) \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\frac {x \left ( -20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}- \left ( {\it \_C2}+{\it \_C6}/2 \right ) \sqrt {x} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( 2\,x \left ( {\it \_C9}-{\it \_C5} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C8}+{\it \_C4} \right ) \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -2\,x \left ( {\it \_C8}-{\it \_C10} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C10}+{\it \_C5} \right ) \right ) \sin \left ( 2/11\,\pi \right ) +2\,\sin \left ( \pi /11 \right ) \left ( x \left ( {\it \_C7}-{\it \_C4} \right ) {a}^{1/11}-1/2\,\sqrt {x} \left ( {\it \_C9}+{\it \_C3} \right ) \right ) \right ) \right ) {{\rm e}^{2\,\cos \left ( 4/11\,\pi \right ) {a}^{1/11}\sqrt {x}}}+ \left ( \left ( -{\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C8}-{\it \_C9} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C5}-{\it \_C6}/2 \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C2}+{\it \_C3} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}-{\it \_C10} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -{\frac {{\it \_C11}}{20790}}-{\it \_C4} \right ) \cos \left ( \pi /11 \right ) +{\it \_C1} \right ) }-{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( {\it \_C7}+{\it \_C9} \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C10}-{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C1}+{\it \_C4} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C8}+{\it \_C6}/2 \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C2}+{\it \_C5} \right ) \cos \left ( \pi /11 \right ) +{\it \_C3} \right ) }+{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C7}-{\it \_C6}/2 \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C8}-{\it \_C2} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\it \_C3}+{\it \_C5} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( -{\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( -{\it \_C10}+{\it \_C1} \right ) \cos \left ( \pi /11 \right ) -{\it \_C4} \right ) }+{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\frac {{\it \_C11}}{20790}}+{\it \_C6}/2 \right ) \cos \left ( 3/11\,\pi \right ) + \left ( {\it \_C9}+{\it \_C1} \right ) \cos \left ( 4/11\,\pi \right ) + \left ( {\it \_C10}-{\it \_C4} \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\it \_C2} \right ) \cos \left ( 2/11\,\pi \right ) + \left ( {\it \_C8}+{\it \_C3} \right ) \cos \left ( \pi /11 \right ) +{\it \_C5} \right ) {a}^{{\frac {5}{11}}}}+ \left ( 2\,x \left ( {\it \_C8}+{\it \_C10} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C10}-{\it \_C5} \right ) \right ) \cos \left ( 3/11\,\pi \right ) + \left ( 2\,x \left ( {\it \_C7}+{\it \_C4} \right ) {a}^{1/11}-\sqrt {x} \left ( {\it \_C9}-{\it \_C3} \right ) \right ) \cos \left ( 4/11\,\pi \right ) + \left ( -{\frac {x \left ( 20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}+\sqrt {x} \left ( -{\it \_C6}/2+{\it \_C2} \right ) \right ) \cos \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 2\,x \left ( {\it \_C9}+{\it \_C5} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C8}-{\it \_C4} \right ) \right ) \cos \left ( 2/11\,\pi \right ) + \left ( 2\, \left ( {\it \_C3}+{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( {\it \_C7}+{\it \_C1} \right ) \right ) \cos \left ( \pi /11 \right ) -{\frac {{\it \_C11}\,\sqrt {x}}{20790}}+2\,{\it \_C2}\,{a}^{1/11}x \right ) \cos \left ( 2\,\sin \left ( {\frac {5\,\pi }{11}} \right ) {a}^{1/11}\sqrt {x} \right ) - \left ( -{\frac {16\,{x}^{3/2}{a}^{2/11}}{9} \left ( \left ( {\it \_C8}+{\it \_C9} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C5}+{\it \_C6}/2 \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C2}+{\it \_C3} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}+{\it \_C10} \right ) \sin \left ( 2/11\,\pi \right ) -{\frac {\sin \left ( \pi /11 \right ) \left ( {\it \_C11}-20790\,{\it \_C4} \right ) }{20790}} \right ) }+{\frac {8\,{a}^{3/11}{x}^{2}}{9} \left ( \left ( {\it \_C7}-{\it \_C9} \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C10}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C1}-{\it \_C4} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C8}-{\it \_C6}/2 \right ) \sin \left ( 2/11\,\pi \right ) -\sin \left ( \pi /11 \right ) \left ( {\it \_C2}-{\it \_C5} \right ) \right ) }+{\frac {16\,{x}^{5/2}{a}^{4/11}}{63} \left ( \left ( {\it \_C7}+{\it \_C6}/2 \right ) \sin \left ( 3/11\,\pi \right ) + \left ( {\it \_C8}+{\it \_C2} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\it \_C3}+{\it \_C5} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C9}-{\frac {{\it \_C11}}{20790}} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C10}+{\it \_C1} \right ) \right ) }-{\frac {32\,{x}^{3}}{945} \left ( \left ( -{\frac {{\it \_C11}}{20790}}-{\it \_C6}/2 \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -{\it \_C9}+{\it \_C1} \right ) \sin \left ( 4/11\,\pi \right ) + \left ( -{\it \_C10}-{\it \_C4} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( {\it \_C7}-{\it \_C2} \right ) \sin \left ( 2/11\,\pi \right ) +\sin \left ( \pi /11 \right ) \left ( {\it \_C8}-{\it \_C3} \right ) \right ) {a}^{{\frac {5}{11}}}}+ \left ( -2\,x \left ( {\it \_C8}-{\it \_C10} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C10}+{\it \_C5} \right ) \right ) \sin \left ( 3/11\,\pi \right ) + \left ( -2\,x \left ( {\it \_C7}-{\it \_C4} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C9}+{\it \_C3} \right ) \right ) \sin \left ( 4/11\,\pi \right ) + \left ( {\frac {x \left ( -20790\,{\it \_C1}+{\it \_C11} \right ) {a}^{1/11}}{10395}}+ \left ( {\it \_C2}+{\it \_C6}/2 \right ) \sqrt {x} \right ) \sin \left ( {\frac {5\,\pi }{11}} \right ) + \left ( 2\,x \left ( {\it \_C9}-{\it \_C5} \right ) {a}^{1/11}+\sqrt {x} \left ( {\it \_C8}+{\it \_C4} \right ) \right ) \sin \left ( 2/11\,\pi \right ) + \left ( -2\, \left ( {\it \_C3}-{\it \_C6}/2 \right ) x{a}^{1/11}+\sqrt {x} \left ( -{\it \_C1}+{\it \_C7} \right ) \right ) \sin \left ( \pi /11 \right ) \right ) \sin \left ( 2\,\sin \left ( {\frac {5\,\pi }{11}} \right ) {a}^{1/11}\sqrt {x} \right ) \right ) {{\rm e}^{-2\,\cos \left ( {\frac {5\,\pi }{11}} \right ) {a}^{1/11}\sqrt {x}}}-{\frac {{\it \_C11}\,\sqrt {x}{{\rm e}^{2\,\sqrt {x}{a}^{1/11}}}}{41580}} \right ) } \right \} \]